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A338127
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Triangle read by rows: T(n,w) is the number of n-step self avoiding walks on a 3D cubic lattice confined between two infinite horizontal planes a distance 2w apart and an orthogonal plane on the y-z axes, where the walk starts at the middle point between the planes on the y-z plane.
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0
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5, 19, 21, 73, 91, 93, 275, 383, 407, 409, 1075, 1639, 1821, 1851, 1853, 4133, 6881, 8019, 8295, 8331, 8333, 16249, 29155, 35507, 37531, 37921, 37963, 37965, 63293, 122491, 155525, 168399, 171691, 172215, 172263, 172265, 249445, 519351, 683711, 758183, 781811, 786823, 787501, 787555, 787557
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OFFSET
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1,1
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LINKS
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FORMULA
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EXAMPLE
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T(2,1) = 19 as after a step in one of the two directions towards the horizontal planes the walk must turn along the planes; this eliminates the 2-step straight walks in those two directions, so the total number of walks is A116904(2) - 2 = 21 - 2 = 19.
The table begins:
5;
19, 21;
73, 91, 93;
275, 383, 407, 409;
1075, 1639, 1821, 1851, 1853;
4133, 6881, 8019, 8295, 8331, 8333;
16249, 29155, 35507, 37531, 37921, 37963, 37965;
63293, 122491, 155525, 168399, 171691, 172215, 172263, 172265;
249445, 519351, 683711, 758183, 781811, 786823, 787501, 787555, 787557;
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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